ENGR Homework 02: Naïve Bayes’ Classifier Solution

In this homework, you will implement a naïve Bayes’ classifier in Python. Here are the steps you need to follow:

    1. Read Section 5.7 from the textbook.

    2. You are given a multivariate classification data set, which contains 35000 clothing images of size 28 pixels × 28 pixels (i.e., 784 pixels). These images are from five distinct classes, namely, T-shirt, Dress, Coat, Shirt, and Bag. The figure below shows five sample clothing images from each class. You are given two data files:

        a. hw02_images.csv: clothing images,

        b. hw02_labels.csv: corresponding image labels (1: T-shirt, 2: Dress, 3: Coat,

4: Shirt, 5: Bag).

























    3. Divide the data set into two parts by assigning the first 30000 images to the training set and the remaining 5000 images to the test set.
deviation parameters
parameters
  ̂!,!,   ̂!,#, … ,   ̂!,$%&, … ,   ̂',!,   ̂',#, … ,   ̂',$%&
,  the  standard
4.  Estimate  the
mean


, … ,   (',!,   (',#, … ,   (',$%&

*
*
  (!,!,   (!,#, … ,   (!,$%&







, and the prior probabilities







(   = 1),…, (   = 5)
using the data
points you assigned to the training set in the





previous step. Your parameter estimations should be similar to the following figures. Please note that, in Section 5.7, the naïve Bayes’ classifier is derived for binary input features. However, in this homework, the input features are assumed to be continuous.

print(sample_means)





[[254.99866667
254.98416667
254.85616667 ...
254.679

254.87816667

254.95933333]






[254.99733333
254.99733333
254.9965
...
254.96883333
254.99216667

254.98866667]






[254.99933333
254.99933333
254.99233333 ...
251.52483333
254.4725

254.97483333]






[254.99666667
254.98983333
254.91416667 ...
252.39516667
254.44166667

254.93666667]






[254.999
254.98433333
254.93783333 ...
250.673

253.23333333

254.79083333]]





print(sample_deviations)





[[
0.09127736
0.25609108
1.31090756 ...  5.29826629
3.9117332

1.93959091]






[
0.2065419
0.2065419
0.2163818
...  1.04076669
0.47057267

0.70062226]






[
0.05163547
0.04081939
0.16002465 ... 18.43665868
6.7881694

1.1061344 ]






[
0.18436076
0.21617116
1.81046936 ... 15.67799977
6.34549162

1.79971911]






[
0.04471018
0.64582342
3.03248555 ... 23.62576428 13.9167006

4.4727787 ]]








print(class_priors)


[0.2 0.2 0.2 0.2 0.2]



    5. Calculate the confusion matrix for the data points in your training set using the parametric classification rule you will develop using the estimated parameters. Your confusion matrix should be the following matrix.

y_truth
1
2
3
4
5
y_pred





1
3685
49
4
679
6
2
1430
5667
1140
1380
532
3
508
208
4670
2948
893
4
234
60
123
687
180
5
143
16
63
306
4389


    6. Calculate the confusion matrix for the data points in your test set using the parametric classification rule you will develop using the estimated parameters. Your confusion matrix should be the following matrix.
y_truth
1
2
3
4
5
y_pred





1
597
6
0
114
1
2
237
955
188
267
81
3
92
25
785
462
167
4
34
11
16
109
29
5
40
3
11
48
722


What to submit: You need to submit your source code in a single file (.py file) and a short report explaining your approach (.doc, .docx, or .pdf file). You will put these two files in a single zip file named as STUDENTID.zip, where STUDENTID should be replaced with your 7-digit student number.

How to submit: Submit the zip file you created to Blackboard. Please follow the exact style mentioned and do not send a zip file named as STUDENTID.zip. Submissions that do not follow these guidelines will not be graded.

Late submission policy: Late submissions will not be graded.

Cheating policy: Very similar submissions will not be graded.